I tend to use targets slightly smaller than the size of the "kill zone" of the animals I hunt. Mostly squares and circles in the 12" & 10" range. Perhaps more important than size is the type of steel used. Mild steel will get beat up real quick. Those calibers will punch a hole i 3/8" steel even at 800 yds. Your best bet would be to order targets made from AR500 steel - the same steel used for armor plating by the military. There are sponsors on this site that sell them. Every now and then, a group buy is available on Snipershide, where they are a real bargain. Money well spent.

I've been told that the hardness or grade of steel is more important than the thickness. I've seen a 338 Edge shooting 300 SMK go clean through 1/2" steel plate at 400 yds, but I believe it to be fairly mild steel.?

That would be A36 steel. We run some Mil-A-46100 and some similar armor at work every now and then. I shot a plate at 100, 200, and 300 yds with 165 grain Barnes Bullet out of a 30.06 and there wasn't even a mark in the material. Draw back is that it sucks to machine.